Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x+2y &= 4 \\ 4x+4y &= 8\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $4x = -4y+8$ Divide both sides by $4$ to isolate $x$ $x = {-y + 2}$ Substitute this expression for $x$ in the first equation. $-7({-y + 2}) + 2y = 4$ $7y - 14 + 2y = 4$ Simplify by combining terms, then solve for $y$ $9y - 14 = 4$ $9y = 18$ $y = 2$ Substitute $2$ for $y$ in the top equation. $-7x+2( 2) = 4$ $-7x+4 = 4$ $-7x = 0$ $x = 0$ The solution is $\enspace x = 0, \enspace y = 2$.